NUMBER

Common Factors

Learn the reliable method for common factors, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Common factors divide two or more numbers exactly; the HCF is the greatest one they share.

Picture itFind every factor pair
2 · THE METHOD

Follow these steps

  1. List the complete factor set for each number.
  2. Mark every factor shared by all the numbers.
  3. For the HCF, choose the greatest shared factor.
3 · WORKED EXAMPLES

See the method in action

Example 1

Which number is a common factor of 4 and 6?

  1. 4 = 2 × 2 and 6 = 2 × 3.
  2. Since 2 and 3 are distinct primes, the greatest common divisor is 2.
Answer: 2
Example 2

There are 36 red beads and 204 blue beads. They are divided into the greatest possible number of identical bags, with none left over. How many bags are made?

  1. 36 = 12 × 3 and 204 = 12 × 17.
  2. Since 3 and 17 are distinct primes, the greatest common divisor is 12.
  3. Each bag contains 3 red and 17 blue beads.
Answer: 12
4 · ELEVENSPRINT TIP

A useful shortcut

For the HCF, choose the greatest shared factor.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.